A neural system is modeled by a MES satisfying the Multiplicity Principle. Its state-categories are obtained by successive complexifications of the category of neurons Neur, and this process adds to the neurons abstract higher order objects, called category-neurons (or cat-neurons).  



A 'simple' cat-neuron emerges as the colimit in a complexification of Neur of a pattern of neurons which has no colimit neuron in Neur, but acts as a synchronous coherent assembly of neurons in the sense of Hebb. An iteration of the process leads to cat-neurons of order 2 which correspond to a super-assembly (or 'assembly of assemblies') of neurons, which cannot be reduced to a (large) synchronous assembly of simple neurons. Higher order cat-neurons in successive complexifications represent super-super-assemblies, and so on.

The explicit construction of the complexification allows to describe the possible interactions between such (super-)assemblies, which cannot be described in classical models: they are the simple and complex links between the corresponding cat-neurons, in those complexifications. So it becomes possible to 'compute' with cat-neurons, i.e., with (super-)assemblies of neurons, as if they were simple neurons, thus developing a real 'algebra of mental objects' (following the proposition of Changeux 1983).

In particular, the Memory of the MES develops in time, under the action of the various CRs, with emergence of more and more complex cat-neurons. Among them, those which store successive strategies and their results form the procedural memory Strat.

Let us remark that this model is very different from neo-connexionnist models of neural systems which give only a description at the sub-symbolic level, and for a limited period, without taking into account the interactions between the different levels. In particular, these models can only describe the formation of simple cat-neurons (represented by attractors of the dynamics), but not their complex links, so that they cannot describe higher order cat-neurons such as those modeling complex mental objects. 

Formation of concepts

The neural system of a more complex animal is able to classify recognized items into invariance classes. To model this classification process in the corresponding MES, we assume that the successive complexifications also add limits, called CR-concepts, classifying invariance classes of items (e.g., of strategies) with respect to some of their attributes.

A CR-concept, for a particular CR, is formed in two phases:

• Firstly, a 'pragmatic' classification: two items are 'acted' as equivalent by a lower CR if their traces in the landscape of the CR activate the same pattern of agents; for instance, in a color-CR, it is the same pattern of receptors which is activated by all blue objects. (Formally, this process is modeled by the notion of 'same shape' in the sense of Borsuk.)

• But this classification takes its meaning only at the level of a higher level CR with a longer period, able to overview what is common to the different items of a class and to store it in the Memory under the form of an object representing the whole class of these items. This object, called a CR-concept (e.g., the color-concept 'blue') is memorized as the limit of the pattern of agents of the lower CR activated by all these items; and its classification domain represents the invariance class of the CR-concept (all the images of blue objects).

A CR-concept can be thought of as an abstract prototype for a class of objects with a 'family resemblance' (in the sense of Wittgenstein); it does not necessitate the existence of a language. 


Semantic Memory

The CR-concepts, with respect to the various CRs, form the Semantic Memory, which is extended by the formation, through successive complexifications, of iterated limits of patterns of CR-concepts, called concepts. First concepts simultaneously classifying several features are formed (as a blue triangle), and then more abstract concepts obtained as limits of patterns of such 'concrete' concepts linked by complex links.

The later re-activation of a concept relies on a double indeterminacy: choice of a particular instance of the concept, then choice of a particular ramification of this instance. Thus the development of a semantic memory adds flexibility to the interplay among the strategies of the CRs. Indeed, concepts representing invariance classes of strategies will be formed in the procedural memory, so that the choice of a strategy by a higher CR will be done under the form of such a concept, instead of a specific strategy of its invariance class. It adds a new liberty degree in the formation of the global strategy S effectively realized on the system at a given time, since it will be possible to select among the strategies of the invariance class chosen by a CR the best adapted one, taking into account the strategies relayed by the other CRs. For instance, the command of a holding motion will be modulated depending on the object to hold. 


Brain/mind problem

The representation of a mental state, such as a complex cognitive process, by a category-neuron of a higher order leads to a new approach of the philosophical problem of the identity between mental states and physical states of the brain. Indeed, a physical state, as it is seen through brain imagery, corresponds only to the activation of a synchronous assembly of neurons, modeled by a simple cat-neuron. But a mental state is represented by a higher order cat-neuron which is non-reducible to a simple one, though it is constructed by successive complexifications from the neuron level, and has ramifications down to this level. So its activation requires a several steps unfolding through the various intermediate levels of a ramification, down to the level of physical states; and at each step, it can proceed along one or another non-equivalent decomposition of multifold objects, with possibly a switch between them, whether of a random origin (neural 'noise') or controlled. Though such a process represents a well described physical 'event', we cannot identify it with a physical 'state': mental states emerge in a dynamic way (through the gradual unfolding of a ramification) from physical states but are not identical to them. This could define an emergentist monism in the sense of Bunge.